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The fatigue crack growth rate can be explained using features of the surface of a structure. Among other methods, linear regression can be used to explain crack growth velocity. Nonlinear transformations of fracture surface texture features may be useful as explanatory variables. Nonetheless, the number of derived explanatory variables increases very quickly, and it is very important to select only few of the best performing ones and prevent overfitting at the same time. To perform selection of the explanatory variables, it is necessary to assess quality of the given sub-model. We use fractographic data to study performance of different information criteria and statistical tests as means of the sub-model quality measurement. Furthermore, to address overfitting, we provide recommendations based on a cross-validation analysis. Among other conclusions, we suggest the Bayesian Information Criterion, which favours sub-models fitting the data considerably well and does not lose the capability to generalize at the same time.
Content available Lévy flights in binary optimization
There are many optimization heuristics which involves mutation operator. Reducing them to binary optimization allows to study properties of binary mutation operator. Modern heuristics yield from Lévy flights behavior, which is a bridge between local search and random shooting in binary space. The paper is oriented to statistical analysis of binary mutation with Lévy flight inside and Quantum Tunneling heuristics.
Content available Generalized semi-opened axial dispersion model
The axial dispersion model (ADM) is studied and then generalized by a new form of the left boundary condition of semi-open flow system. The resulting parameter driven model covers the traditional axial models: axial closed-opened dispersion model with enforced input concentration (AEO), axial closed-opened dispersion model with input Danckwerts' condition (ACO), and axial opened-opened model (AOO). It also enables development of the degraded axial model (ADO). The research is concerned with both modeling and mathematical solution. Also, many numerical aspects of computer realization are discussed.
The paper is oriented to EEG signal analysis, which is focused to quasi-stationarity hypothesis that the statistical properties of the channel signal fluctuate in time. Robust linear predictor is used for short segments of EEG as low-pass filter and the difference between the raw EEG and filter output was subject of statistical testing. Novelty is in the fluctuation measurement which enables to classify the Alzheimer's disease patients against controls.
Content available remote Axial dispersion models and their basic properties
The paper is oriented to summary of important basic relations, which characterize behavior of four axial dispersion models (AEO: axial enforced closed-open model, ACO: axial closed-open model, ACC: axial closed-closed model, AOO: axial open-open model) and three referential models (ideal mixed model, plug flow model, cascade of ideal mixers without back-mixing). Selected basic properties (parametric characteristics) of these models can be used for parameter identification of included hydrodynamic flow structure models. Mathematical description of models including initial and boundary conditions, transfer function, model transient response to Dirac impulse as weighting (impulse) function, model transient response to step function as step response are included in this study. There are also included further characteristics of impulse function: raw moments up to 4th order, variance, variation coefficient, skewness , kurtosis, location and value of mode. Complete set of these characteristics for all studied models is collected (model-by-model) in seven tables. The authors declare several properties of weighting function as key ones: value of 1st raw (dimensional) moment, parametric values and mode properties, related to dependence on Peclet number. The plots of parametric values and mode properties vs. Peclet number are mentioned in the paper for four studied axial dispersion models.
Content available remote Useful approximation of discrete transcedent transfer function
Linear systems with distributed parameters are described via linear partial differential equations. The application of Laplace transform comes to discrete transcendent transfer functions. When the response to unit step is aperiodic then the transfer function can be approximated by the system of second order with time delay. The role of sampling period is studied on four examples of heat and mass transfer systems. The methodology is based on inverse Laplace transform, sampling, Z transform and properties of power series. A new useful lemma was developed to help with error approximation. All the calculations were performed in the Matlab environment.
Content available remote Affine invariant 2D recognition in grain classification
Invariant recognition of 2D binary image often arises from image moments. They enable the construction of affine transform, which ensures the invariance to translation, scaling, first rotation and stretching of the image. It is a problem to ensure the invariance to the second rotation. The paper deals with two methods how to realize the affine invariant recognition system with the numerical stable elimination of the second rotation. Modified images are obtained via polar or Radon's transform. Mentioned two approaches enable affine invariant systems construction and they were used for analysis of particles in granular mixtures. The affine invariant system is applied to detail analysis of fertilizer grains.
Content available remote Lipschitz continuity of fuzzy controller
Any traditional fuzzy controller performs a sequence of three processes: fuzzification, control algorithm and defuzzification. It is useful when the contoller exhibits continuous behavior with constrained output and sensitivity. After the normalization of controller inputs and outputs into the interval [0;1], we designed the fuzzy controller to be Lipschitz continuous, which implies the constrained sensitivity of the controller. Łukasiewicz algebra enriched by ŁAsqrt was used for the realization of the proposed fuzzy controller. The realization of fuzzification and control algotithm is trivial. The only problem is in the defuzzification. Neither Mamdani nor Larsen approaches are continuous in general. Both MOM and COG technoques generate discontinuous output behaviour. That is why we developed a new defuzzification method based on Łukasiewicz algebra. Thus, the proposed technique of defuzzification is based on propositional logic and it helps to realize a class of Lipschitz continuous fuzzy controllers. the controllers were realized in the Matlab environment.
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